Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x-3y &= 5 \\ 3x+9y &= -9\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $3x = -9y-9$ Divide both sides by $3$ to isolate $x$ $x = {-3y - 3}$ Substitute this expression for $x$ in the first equation. $-5({-3y - 3}) - 3y = 5$ $15y + 15 - 3y = 5$ Simplify by combining terms, then solve for $y$ $12y + 15 = 5$ $12y = -10$ $y = -\dfrac{5}{6}$ Substitute $-\dfrac{5}{6}$ for $y$ in the top equation. $-5x-3( -\dfrac{5}{6}) = 5$ $-5x+\dfrac{5}{2} = 5$ $-5x = \dfrac{5}{2}$ $x = -\dfrac{1}{2}$ The solution is $\enspace x = -\dfrac{1}{2}, \enspace y = -\dfrac{5}{6}$.